72 - 74 Light intensity of illumination and theory of attraction

Problem 72
A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is

$I = \dfrac{k \sin \theta}{d^2}$

where θ is the angle of incidence and d the distance from the source.)